Complex and Kahler geometry

Complex geometry and complex-analytic spaces

Huybrechs, Complex geometry: an introduction

Demailly, Complex-analytic and differential geometry

Wells, Differential analysis on complex manifolds

Zheng, Complex differential geometry

Fischer, Complex analytic geometry

Lojasiewicz, Introduction to complex analytic geometry

Grauert and Remmert, Coherent analytic sheaves

Kahler manifolds

Ballmann, Lectures on Kahler manifolds

Moroianu, Lectures on Kahler geometry

A mix of everything:

Griffiths and Harris, Principles of algebraic geometry